Constant mean curvature discs with bounded area

López, Rafael; Montiel, Sebastián

doi:10.1090/S0002-9939-1995-1286001-0

Constant mean curvature discs with bounded area
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by Rafael López and Sebastián Montiel PDF

Proc. Amer. Math. Soc. 123 (1995), 1555-1558 Request permission

Abstract:

It has been long conjectured that the two spherical caps are then only discs in the Euclidean three-space ${\mathbb {R}^3}$ with non-zero constant mean curvature spanning a round circle. In this work, we prove that it is true when the area of such a disc is less than or equal to that of the big spherical cap.

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